Formation of Micelles in Homopolymer-Copolymer Mixtures: Quantitative Comparison between Simulations of Long Chains and Self-Consistent Field Calculations

Abstract

Using Monte Carlo simulations of the bond fluctuation model and self-consistent field calculations, we study the formation of micelles in a mixture of homopolymers and asymmetric AB-diblock copolymers with composition, fA = 1/8. Both types of molecules are fully flexible and have identical length. We work in the semi-grand-canonical ensemble, i.e., we fix the monomer density and incompatibility, χN ≃ 100 (strong segregation regime), and control the composition of the mixture via the exchange chemical potential, δμ ≡ μAB − μB between the copolymers and homopolymers. The Monte Carlo simulation comprises moves that allow homopolymers to mutate into AB-diblock copolymers and vice versa. These moves are very efficient in equilibrating the configurations. We accurately locate the critical micelle concentration, study the micellar size distribution and characterize the shape of the micelles by the tensor of gyration and radial density profiles. The results of the simulations are quantitatively compared to predictions of the self-consistent field theory in the grand-canonical ensemble without adjustable parameters. Only in the limit of high molecular weight the simulation results gradually approach the theoretical predictions.